%0 Report %D 2018 %T Foldable structures made of hydrogel bilayers %A Virginia Agostiniani %A Antonio DeSimone %A Alessandro Lucantonio %A Danka Lučić %G eng %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %T Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets %A Virginia Agostiniani %A Alessandro Lucantonio %A Danka Lučić %B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %G eng %R https://doi.org/10.1051/cocv/2018046 %0 Report %D 2013 %T Attainment results for nematic elastomers %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %X We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. %I SISSA %G en %U http://hdl.handle.net/1963/7174 %1 7201 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-10-22T14:32:26Z No. of bitstreams: 1 Ago-DM-DeS-13-sissa.pdf: 394672 bytes, checksum: d02690a6c7f206310d28d253ce53d0d3 (MD5) %0 Journal Article %J Ann. Inst. H. Poincare Anal. Non Lineaire %D 2012 %T Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %K Nonlinear elasticity %X

The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

%B Ann. Inst. H. Poincare Anal. Non Lineaire %I Gauthier-Villars;Elsevier %V 29 %P 715-735 %G en %U http://hdl.handle.net/1963/4267 %1 3996 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T15:11:45Z\\r\\nNo. of bitstreams: 1\\r\\nAgostiniani_DalMaso_30_M.pdf: 407057 bytes, checksum: 2009d1218f7735191a1c768a73b400a3 (MD5) %R 10.1016/j.anihpc.2012.04.001 %0 Journal Article %J International Journal of Non-Linear mechanics %D 2012 %T Ogden-type energies for nematic elastomers %A Virginia Agostiniani %A Antonio DeSimone %K Nonlinear elasticity %X

Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

%B International Journal of Non-Linear mechanics %I Elsevier %V 47 %P 402-412 %G en %N 2 %1 6971 %2 Mathematics %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2013-07-15T14:33:38Z No. of bitstreams: 0 %R 10.1016/j.ijnonlinmec.2011.10.001 %0 Journal Article %J Discrete & Continuous Dynamical Systems - A %D 2012 %T Second order approximations of quasistatic evolution problems in finite dimension %A Virginia Agostiniani %K discrete approximations %K perturbation methods %K saddle-node bifurcation %K Singular perturbations %K vanishing viscosity %X

In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.

%B Discrete & Continuous Dynamical Systems - A %V 32 %P 1125 %G eng %U http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8 %R 10.3934/dcds.2012.32.1125 %0 Journal Article %J Continuum. Mech. Therm. %D 2011 %T Gamma-convergence of energies for nematic elastomers in the small strain limit %A Virginia Agostiniani %A Antonio DeSimone %K Liquid crystals %X

We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

%B Continuum. Mech. Therm. %I Springer %V 23 %G en %U http://hdl.handle.net/1963/4141 %1 3882 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-15T13:10:38Z\\nNo. of bitstreams: 1\\nAgost_DeSim07M.pdf: 348761 bytes, checksum: b9b69eb7da7ca6962e4a46e904646a6b (MD5) %& 257 %R 10.1007/s00161-011-0180-2